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Some Poisson Approximations Using Compensators
- Source :
- Ann. Probab. 11, no. 3 (1983), 726-744
- Publication Year :
- 1983
- Publisher :
- Institute of Mathematical Statistics, 1983.
-
Abstract
- We give new results on the total variation distance of the distribution of a point process on the line from that of a Poisson process. Both one dimensional and function space distances are considered. Additionally similar bounds for marked point processes are given, both for the finite and infinite mark space cases. The bounds are all given in terms of the compensator of the point process (with respect to an arbitrary filtration) and are analogues and extensions of discrete time results of Freedman (1974) and Serfling (1975). Some new techniques for discrete approximation of compensators are used in the proofs. Examples of the use of the bounds appear elsewhere (Brown and Pollett, 1982, Brown, 1981), but an application to compound Poisson approximation and thinning of point processes is given here.
- Subjects :
- Statistics and Probability
marks
Mathematical analysis
Discrete Poisson equation
Poisson process
Poisson distribution
Point process
symbols.namesake
Compound Poisson distribution
Uniqueness theorem for Poisson's equation
60G07
Compound Poisson process
symbols
Zero-inflated model
discrete approximations
60G55
60G44
compensator
Statistics, Probability and Uncertainty
Fractional Poisson process
Mathematics
Subjects
Details
- ISSN :
- 00911798
- Volume :
- 11
- Database :
- OpenAIRE
- Journal :
- The Annals of Probability
- Accession number :
- edsair.doi.dedup.....76002aecd27a1f739992335a71a6098b